System Specifications for Attitude Determination and Control System

System Specifications for Attitude Determination and Control System PPE-CDC-ADCS_1693 ECE Paris Page 1

Version Date Paged Modified Observations 0.1 05/10/2016 All Creation of the document. Global part, ADCS System 0.2 21/02/2017 Algorithm One page algorithm PPE-CDC-ADCS_1693 ECE Paris Page 2

TABLE OF CONTENT I. Terminology... 5 II. Global project... 6 1. Space debris... 6 2. CubeSat... 7 3. Subsystems from CubeSat... 8 III. ADCS... 9 1. ADCS functionality... 9 2. ADCS Modules... 10 a) Sensors System (SENS)... 11 b) Actuators System (ACT)... 11 c) Controller (CTRL)... 11 d) Interface (INT)... 11 3. Recap on ADCS... 11 IV. Requirements... 13 1. Applicable standards... 13 2. Requirement level... 13 3. ADCS Requirements... 14 a) Global ADCS Requirements... 14 b) Actuators System Requirements... 14 c) Sensors System Requirements... 15 d) Controller Requirements... 16 V. ADCS Scenarios description... 17 1. SENS scenarios... 17 2. ACT scenarios... 23 3. CTRL scenarios... 24 PPE-CDC-ADCS_1693 ECE Paris Page 3

VI. State of the Art... 26 1. Positioning method and algorithm:... 26 a) Euler angles:... 27 b) Gimbal angles:... 28 c) Quaternions:... 29 d) Measuring the attitude:... 29 e) TRIAD Algorithm:... 31 f) Kalman Filter:... 32 2. Sensors:... 33 a) Gyroscope... 33 b) Gyrometer... 35 c) Sun sensor... 36 d) Star tracker... 37 e) Horizon sensor... 38 f) Magnetometer... 38 g) Temperature sensors... 40 h) Summary... 42 3. Actuators:... 43 a) Reaction wheel... 43 b) Momentum wheel... 43 c) Control momentum gyroscope... 44 d) Magnetorquer... 44 e) Permanent magnet... 46 4. Electronic board: State of the art... 47 a) Hardware... 47 b) Hardware constraint... 48 c) Software approach... 49 5. Simulations... 50 VII. Planning... 53 VIII. Technical sizing... 54 IX. Existing CubeSat... 57 PPE-CDC-ADCS_1693 ECE Paris Page 4

I. Terminology ADCS: CTRL: ECE: EDT: EPS: ESA: ISS: LEO: OBC: PV: PSS: SENS: TBD: TCS: Attitude Determination and Control System ADCS Controller Ecole Centrale d Electronique Electrodynamic Tether Electrical Power System European Space Agency International Space Station Low Earth Orbit On-Board Computer Photovoltaïc Photosensors Set ADCS Sensors System To Be Determined Telecommunication System PPE-CDC-ADCS_1693 ECE Paris Page 5

II. Global project 1. Space debris Since the beginning of the space race in 1957, the number of objects sent into orbit is continuously growing, as does the amount of space debris orbiting the Earth. This is becoming a real threat for operational space missions around the Earth. Space debris can be the result of: A collision between 2 satellites, 2 debris or a satellite and a debris/meteoroid A battery which became unstable and exploded Fuel leftovers in a satellite or a launcher stage which became unstable and exploded A planned destruction An out of control satellite or a launcher stage Today, the population of space debris is estimated to be more than 500 000 trackable objects where 20 000 of them are bigger than a tennis ball. In addition, there are millions of pieces too small to be detected. The vast majority of space debris is located in Low Earth Orbit (LEO) where most space missions are located or planned. Figure 1 illustrates the distribution of debris around the Earth in 2013. Figure 1 : Representation of the distribution of the space debris in LEO in 2013. Source: ESA Even with the direct threat to space missions that space debris represents, the real threat comes in the long-term management of the Earth orbit. Indeed, the Clean Space department of ESA calculated that the population of debris would keep on growing in an exponential way if the space industry does not change or if every space activity stops (Figure 2); thus preventing any orbital activity. The same forecast considered the limitation of debris creation, End of Life (EOL) management, debris removal (Figure 3) and the limitation of orbital objects. Figure 2 : Space debris population forecast in 2209 if nothing is done to mitigate them. Figure 3 : Space debris population forecast in 2209 if space debris mitigation is implemented. PPE-CDC-ADCS_1693 ECE Paris Page 6

One part of the implementation of the space debris mitigation is made through the development of solutions to give the tools to the new satellites to perform deorbiting maneuvers to either cemetery orbits where the satellite is passivated (batteries and tanks emptied) or toward Earth to disintegrate upon re-entry into the atmosphere. Several types of deorbiting systems are currently being developed such as the aerodynamic sail, chemical engine, and electric/ionic engine. 2. CubeSat A CubeSat is a nanosatellite respecting a standard set by California Polytechnic State University stating that a one unit (1U) CubeSat has a strict volume of 1L within a cube of 10 cm and a mass equal or lesser than 1.33 kg. It is possible to increase the size of a CubeSat by adding units. For example, CubeSat composed two units (2U) and 3U CubeSat and more are obtained this way. CubeSats are very attractive due to their development speed and their low costs but it is often done with little regard to quality and a lot of them fail in their missions, thus becoming space debris. A CubeSat in lower earth orbit around 400 km will naturally deorbit within a few months but when the altitude rises, around 600 km, natural deorbiting takes more time and does not respect the 25 years rule (Figure 4). Figure 4 : Lifetime of CubeSat in orbit regarding its altitude. PPE-CDC-ADCS_1693 ECE Paris Page 7

3. Subsystems from CubeSat The ECE³SAT system is divided in subsystems to facilitate the work. So in each subsystem there are specific objectives. And each subsystem remains linked to the other subsystems. All subsystems: EPS ADCS OBC TCS EDT EPS OBC TCS Ground Station ADCS EDT Data Transfer Figure 5 : Links between subsystems PPE-CDC-ADCS_1693 ECE Paris Page 8

Sensors Project ECE 3 SAT III. ADCS 1. ADCS functionality The ADCS has a support role through the CubeSat mission. He has to maintain all other modules in an operational situation. So as an entry it takes the sensors and as an output it uses actuators. Phase 1 Phase 2 Phase 3 Current attitude determination Desired attitude determination Needed movement determination (Yaw/Pitch/Roll) Control of Actuators Actuators Figure 6 : ADCS Functioning PPE-CDC-ADCS_1693 ECE Paris Page 9

EPS Sensors OBC Project ECE 3 SAT 2. ADCS Modules The ADCS is divided into 4 modules. It is important to note that the ADCS system is currently based on a preliminary design and is subject to changes. The objectives of each module are depicted in the following list: The SENS is composed of a set of sensors. This set will have to harvest data in order to get information about the CubeSat position. The ACT are the CubeSat attitude actuators. ACT will have to adapt the CubeSat s attitude according to the mission needs. The ADCS controller objectives are to collect data from sensors and to process it to get reliable positioning information. Then the ADCS will send orders to ACT in order to correct/modify the CubeSat s attitude if OBC and EPS subsystems allow it. The Interface module has for objective to ensure good connection with other systems of the satellite and to send data to the other systems. ADCS Subsystem Micro controller (Algorithm) OBC Signal processing interface Actuators Power control interface Data Electrical power Figure 7 : ADCS module dependence PPE-CDC-ADCS_1693 ECE Paris Page 10

a) Sensors System (SENS) ADCS Sensors system will be composed of absolute sensors to get constant access to the attitude relative to an external frame. And relative sensors to get access to the current attitude relative to the previous one. b) Actuators System (ACT) The actuators goal is to position the CubeSat in the target attitude by rotation it around 3 axes. Yaw / Pitch / Roll So the Actuators System will be placed to have control over the 3 axes (X, Y, Z). c) Controller (CTRL) The ADCS Controller will calculate the attitude in which the CubeSat is thanks to the data coming from Sensors. Also the Algorithm inside the controller will calculate the targeted attitude. And then will determine the rotations to accomplish for each axis. d) Interface (INT) The ADCS Interface is the hardware part of ADCS which transmit the signal received from Sensors to the micro-controller and it also distributes power supply coming from the EPS subsystem to the Actuators. 3. Recap on ADCS ADCS Sensors Actuators Controller Interface Absolute Sensors Relative Sensors 3 axis actuator system Rotation Calculate current attitude Calculate desired attitude Signal distribution Alimentation distribution Send orders Figure 8 : ADCS module division PPE-CDC-ADCS_1693 ECE Paris Page 11

ADCS Algorithm OBC Communication Initialization Sensors and Actuators Initialization Start I0 Initialization Transfer ACT and SENS state to OBC Actuators in progress Measures in progress Stop Actuators Stop measures Order to stop Actuator actions Order to stop measures OBC Order Order to start Send Actuator order to the Order to start Send measures to Actuators in progress Measures in progress Control measures Control measures Start Actuators Order to shut down Start measures Actuators in progress End Start measures Measures in progress PPE-CDC-ADCS_1693 ECE Paris Page 12

IV. Requirements 1. Applicable standards ECSS-Q-ST-40C o Safety/Launch authority safety requirements ECSS-Q-70-71A o Data for selection of space materials and processes ESA-ADMIN-IPOL (2014)2 o Space Debris Mitigation for Agency Projects 2. Requirement level Requirement level Shall Should May Definition The word shall indicates mandatory requirements strictly to be followed in order to conform to the standard and from which no deviation is permitted (shall equals is required to). First order of importance. The requirement is vital. It must be validated in priority. The word should indicates that among several possibilities one is recommended as particularly suitable, without mentioning or excluding others; or that a certain course of action is preferred but not necessarily required (should equals is recommended that). It is a second level of importance. It means that a Should requirement must be validated after a Shall requirement. The word may is used to indicate a course of action permissible within the limits of the standard (may equals is permitted to). It is a third order of importance. The requirement is a plus to the system. A may requirement must be validated after a Should requirement. PPE-CDC-ADCS_1693 ECE Paris Page 13

3. ADCS Requirements a) Global ADCS Requirements RQ CODE Requirement name Details Level RQ01-ADCS Each ADCS system has to switch ON on OBC orders. The OBC activates the CTRL to control ADCS system Shall RQ02-ADCS Each ADCS system has to switch OFF on OBC orders. This is to prevent any issues from compromising the mission. Shall RQ03-ADCS Each ADCS system has to be shielded against environmental disturbance. Resistance against high and low temperatures, radiations and magnetic fields. Shall RQ04-ADCS Each part of ADCS system has to not interfere with other modules from CubeSat. Do not disturb other modules in an unintended way. Shall RQ05-ADCS The ADCS module shall fit inside of the CubeSat Shall RQ06-ADCS The ADCS module shall have a limited mass Shall RQ07-ADCS The ADCS module shall have a limited power consumption Shall b) Actuators System Requirements RQ CODE Requirement name Details Level RQ01-ACT RQ02- ACT ACT has to be turned ON and OFF on CTRL order. ACT has an independent action on each axis. The OBC activates the CTRL which activates the ACT. Means the 3 axis are independently controller. RQ03- ACT ACT must orientate CubeSat to have EDT Shall module facing the Earth. RQ04- ACT ACT should position with precision. Need to have a good orientation. Should Shall Shall PPE-CDC-ADCS_1693 ECE Paris Page 14

c) Sensors System Requirements RQ CODE Requirement name Details Level RQ01-SENS SENS has to be turned ON and OFF on CTRL orders. The OBC activates the CTRL which activates the SENS. RQ02-SENS SENS has to send data to the CTRL. The data collected will be sent to CTRL. RQ03-SENS RQ04-SENS RQ05-SENS RQ06-SENS SENS has to be able to realize a measurement session with only one type of sensor (GSCS, PSS, MMS). SENS has to realize a complete measurement session on CTRL order. A specific warning is sent to CTRL for each sensor if it gives inaccurate measure. A specific warning is sent to CTRL for each sensor if it fails. The measurement session will be able to ask data from only one sensor A measurement session means that SENS will be activated to collect data. Depends on the kind of sensor, some do analyze their values. Different warnings to turn OFF the right sensor. RQ07-SENS SENS should be redundant. Should RQ08-SENS SENS has a fast answer time. Should Shall Shall Shall Shall Shall Shall RQ09-SENS SENS hardware is low power consumption and lightweight. Also, means the less possible pins. Should PPE-CDC-ADCS_1693 ECE Paris Page 15

d) Controller Requirements RQ CODE Requirement name Details Level RQ01-CTRL CTRL has to react accordingly to the The OBC is the headmaster. Shall process order sent by OBC. RQ02-CTRL CTRL has to send SENS s processed data to the OBC. Data from sensors can be used by all modules. Shall RQ03-CTRL CTRL has to manage each ADCS The ADCS system will be made of Shall system independently. functions inside the CTRL allowing all parts to be independent. RQ04-CTRL CTRL has to process the SENS s data. Data coming from the SENS s. Shall RQ05-CTRL CTRL has to give orders to ACT. Orders like ON/ OFF and also for Shall positioning each axis RQ06-CTRL CTRL has to send periodically an OBC needs to know if there are Shall activity report to the OBC. issues in ADCS. RQ07-CTRL CTRL has to be able to determine the Algorithm to get the current Shall actual attitude. attitude. RQ08-CTRL CTRL has to be able to determine the Algorithm giving the wanted Shall wanted attitude. attitude. RQ09-CTRL CTRL has to be able to determine the correction necessary on the attitude. Algorithm giving the correction to apply on ACT s. Shall PPE-CDC-ADCS_1693 ECE Paris Page 16

V. ADCS Scenarios description 1. SENS scenarios SC01_SENS Requirements: Initial conditions: Scenario: External interface used: Exit conditions: RQ03-SENS, RQ05-SENS, RQ07-SENS, RQ06-SENS SENS is responding to orders from CTRL. SC01-SENS: SENS has to send data to the CTRL. Order from the CTRL, Energy from the CTRL CTRL sends inactive order TC01-SENS: Test if SENS activates on CTRL orders. Test cases TC02-SENS: Test if SENS reacts accordingly to CTRL orders. TC03-SENS: Test if SENS inactivates on CTRL orders SC02-SENS Requirements: Initial conditions: Scenario: External interface used: Exit conditions: Test cases RQ05-SENS, RQ06-SENS, RQ07-SENS One sensor measurement does not match the expected range of the measured phenomenon. SC02-SENS: Determination of the questioned sensor and warning raising to the CTRL. Order from the CTRL, Energy from the CTRL CTRL adds this sensor to the black list. TC04-SENS: Test if sensors sends warning to the CTRL if out range measurements. PPE-CDC-ADCS_1693 ECE Paris Page 17

SC03-SENS Requirement: Initial conditions: Scenario: External interface used: Exit conditions: Test cases RQ03-SENS, RQ04-SENS, RQ05-SENS, RQ06-SENS, RQ07-SENS One sensor measurement does not respond to CTRL order. SC03-SENS: Determination of the questioned sensor and alert raising to the CTRL. Order from the CTRL, Energy from the CTRL CTRL adds this sensor to the black list. TC05-SENS: Test if SENS sends alerts or respond to CTRL. SC04-SENS Requirements: Initial conditions: Scenario: External interface used: Exit conditions: Test cases RQ03-SENS, RQ04-SENS, RQ05-SENS SENS gets orders from CTRL. SC04-SENS: SENS measures the light intensity. Values transmitted are almost null. Order from CTRL, Power from the CTRL. SENS don t detect sun light, CS hiding from sunlight. TC06-SENS: Test if SENS goes to sunlight mode. PPE-CDC-ADCS_1693 ECE Paris Page 18

SC05-SENS Requirements: Initial conditions: Scenario: External interface used: Exit conditions: Test cases TBD After measurement, solar and magnetic vectors are collinear and ADCS can t describe CS position. SC05-SENS: The determinist algorithm is offline and CS use only Kalman Extended Filter and GSCS are used to estimate attitude. Order from CTRL, Power from the CTRL. Both vectors are non-collinear. Determinist algorithm is back online. TC08-SENS: Test if collinear vectors are detected. SC06-SENS Requirement: Initial conditions: TBD One actuator is not responding to the CTRL. SC06-SENS: All ACTs are switched off, Kalman Extended Filter and Scenario: GSCS are used instead as attitude estimation. TLE data should be sent in accelerated rate to avoid too much error in estimation. External interface used: Exit conditions: Test cases Power from the CTRL The ACT is responding to the CTRL or specific new order from the CTRL. TC09-SENS: Test if the ACTs goes offline as requested by CTRL PPE-CDC-ADCS_1693 ECE Paris Page 19

SC07-SENS Requirements: Initial conditions: Scenario: External interface used: Exit conditions: Test cases TBD CS is launched, one PSS is not responding to the CTRL. SC07-SENS: The corresponding PV panel is used instead of the PS for calculation Power from the CTRL The PSS is responding to the CTRL or specific new order from the CTRL. TC10-SENS: Test if ADCS gets measure of PV panels. SC08-SENS Requirements: Initial conditions: Scenario: External interface used: Exit conditions: Test cases TBD One PSS is not responding to the CTRL. SC08-SENS: The CTRL put the PSS offline, Kalman extended filters and GSCS are used instead for attitude estimation. Power from the CTRL The PSS is responding to the CTRL or specific new order from the CTRL. TC11-SENS: Test if ADCS gets measure of PV panels. PPE-CDC-ADCS_1693 ECE Paris Page 20

SC09-SENS Requirements: Initial conditions: Scenario: External interface used: Exit conditions: Test cases TBD One GSCS is not responding to the CTRL in detumbling mode. SC09-SENS: The detumbling is done with the axis remaining. Then MMS and PSS are used to detumble the last axis. Power from the CTRL The GSCS is responding to the CTRL or specific new order from the CTRL. TC11-SENS: Test if MMS and PSS can calculate angular rates. SC10-SENS Requirements: Initial conditions: Scenario: External interface used: Exit conditions: Test cases TBD CS is launched, one GSCS is not responding to the CTRL in non detumbling mode. SC10-SENS: CTRL send the GSCS offline Power from the CTRL The GSCS is responding to the CTRL or specific new order from the CTRL. TC11-SENS: Test if MMS and PSS can calculate angular rates. PPE-CDC-ADCS_1693 ECE Paris Page 21

SC11-SENS Requirements: Initial conditions: Scenario: External interface used: Exit conditions: Test cases TBD CS is launched, no initial parameters are given to CS and attitude estimation can t be done SC11-SENS: SENS measurement rate is slowing down and are stocked in CTRL and not treated Power from the CTRL Initial parameters are sent TC11-SENS: Test if SENS is changing rate with no initial parameters PPE-CDC-ADCS_1693 ECE Paris Page 22

2. ACT scenarios SC01-ACT Requirements: Initial conditions: Scenario: External interface used: Exit conditions: TBD CS is launched but the attitude does not match with the expectation. SC01-ACT: Determination of the failure Order (energy) from the CTRL CTRL sends inactive order; the failure is founded TCO1- ACT: Test if MTS activates on CTRL orders Test cases TC02- ACT: Test if MTS reacts accordingly to CTRL orders TC03- ACT: Test if MTS inactivates on CTRL orders TC04- ACT: Test the reaction of each MT PPE-CDC-ADCS_1693 ECE Paris Page 23

3. CTRL scenarios SC01-CTRL Requirements: Initial conditions: Scenario: External interface used: Exit conditions: Test cases TBD CTRL has received and processed data from SENS and they are inaccurate SC01-CTRL: CTRL raises a warning to the OBC CTRL/OBC/ SENS CTRL sent the warning to the OBC TCO1-CTRL: Test if CTRL figures out inaccurate data SENS TC02-CTRL: Test if CTRL can send a proper warning to the OBC SC02-CTRL Requirement: Initial conditions: Scenario: External interface used: Exit conditions: Test cases TBD CTRL did not receive an expected answer from the SENS SC02-CTRL: CTRL raises a specific alert to the OBC CTRL/OBC/ SENS CTRL sent the alert to the OBC TCO3-CTRL: test if CTRL figures out if an SENS failed TC02-CTRL: Test if CTRL can send a proper alert to the OBC PPE-CDC-ADCS_1693 ECE Paris Page 24

SC03-CTRL Requirements: Initial conditions: Scenario: External interface used: Exit conditions: TBD CTRL has figured out that the current attitude isn t matching expectation. SC03-CTRL: CTRL raises a specific alert to the OBC CTRL/OBC/ SENS CTRL sent the alert to the OBC TCO5-CTRL: test if CTRL figures out an attitude which doesn t match Test cases with expectation. TC02-CTRL: Test if CTRL can send a proper alert to the OBC. SC04-CTRL Requirement: Initial conditions: Scenario: External interface used: Exit conditions: Test cases TBD CTRL did not receive any answer from the OBC SC04-CTRL: CTRL is switching to Stand-by mode and ping the OBC periodically CTRL/OBC CTRL receives an order from the OBC TCO6-CTRL: turn on the ADCS whereas the OBC is shut down and then switch the OBC on. PPE-CDC-ADCS_1693 ECE Paris Page 25

VI. State of the Art The state of the art is included in the specifications and describe the functionalities described in part ADCS. 1. Positioning method and algorithm: Needs: Calculate CubeSat orientation: o Estimate an angular rotation Determine the trajectory to have, to reach the desired orientation. Calculate the orientation: o Chose the priority (solar productivity / Tether orientation) o Determine the most interesting position Traduce it in physical input for actuators Representation of attitude for a system: To fix the attitude of any object we first need reference frame called (X, Y, Z) and then a frame for our mobile system (X, Y, Z ). PPE-CDC-ADCS_1693 ECE Paris Page 26

a) Euler angles: OXYZ basis is related to solid OX'Y'Z 'by three successive rotations: -The Precession around Oz (going from OXYZ to OUVZ) -The Wobble around OR (going from OUVZ to OUWZ ') -The Own rotation around OZ '(going from OUWZ' to OX'Y'Z ') Then the instantaneous rotation vector is: Figure 9 : Euler Angles representation Thus, any vector x in a given base can be expressed in another frame as a composition of rotations: PPE-CDC-ADCS_1693 ECE Paris Page 27

With vectors of rotation: However, there are singular points that prevent the orientation calculation in certain positions. Indeed, when the second rotation around the axis u is zero or multiple of π, it is impossible to differentiate the two other rotations because in this case the Z and Z ' axes are confused (related to cosine / sine) And with the composition of rotations it is possible to set up symmetrical rotations {R121, R131, R212, R232, R313, R323} and antisymmetric rotations or gimbal angles {R123, R132, R213, R231, R312, R321} b) Gimbal angles: - roll angle (around X) defined in [-π, π] - pitch angle (around Y) defined in [-π / 2, π / 2] - yaw angle (around Z) defined in [-π, π] As the Euler angles, the gimbal angles contain points called "Gimbal lock" (when the second angle theta is equal to +/- π / 2) There are other representations which have no singular points (such as the representation of quaternions). PPE-CDC-ADCS_1693 ECE Paris Page 28

c) Quaternions: This representation, unlike the Euler Angles, is not intuitive at all but the associated calculations are less complex. Thus it requires less computation power, time and less energy. The quaternions respect the following properties: The rotation quaternion is represented as such: Where in rad. is a normalized vector that gives the direction of the rotation axis and α is the rotation angle To rotate any vector around the axis by the α angle, we can apply the following equation: Where is the rotated vector. In our case, we have the initial and the final attitude ( and ). We can use the quaternion representation to get the rotation quaternion ( ) with relatively simple operations from a computational point of view. We can then deduce the rotation axis and angle and convert them to the Euler angle format, that we can use to calculate the output to the actuators. d) Measuring the attitude: Two non-collinear and non-zero vectors within two frames are sufficient to determine the attitude of a solid. In many systems they point on far fixed stars from the system (using Star Tracker), the Sun (using Sun sensors), or the Earth (using magnetometer and Earth sensors). In the terrestrial reference frame, the magnetic fields and the gravitational acceleration are known eg Paris g = 9.81 m/s and Bh = 20.6μT and Bv = 42.24μT with: PPE-CDC-ADCS_1693 ECE Paris Page 29

We must then measure the vectors of two fields in the mobile frame. Let s call A the accelerations on each axis and M the magnetometers measurements on the axis: By developing: Then, using the Gimbal angles (R 321) the equations are obtained: Solving the system: Arctg 2 is equivalent to Arctg on - π / π This method is rarely used because it requires a large number of trigonometric calculations. PPE-CDC-ADCS_1693 ECE Paris Page 30

e) TRIAD Algorithm: Triad algorithm is one of the earliest and simplest solutions to the spacecraft attitude determination problem. It consists in constructing two orthonormal bases using two pairs of vector measurements. Two in the orbital reference frame, noted and and two in the body reference frame, noted and, representing the same magnitude expressed in a different referential. The following equations are used to build referential and the basis attached to the orbital referential., the basis attached to the body Figure 10 : [t1b t2b t3b] are represented in black and [t1r t2r t3r] in green Given the knowledge of two vectors in the reference and body coordinates of a satellite, the TRIAD (TRIaxis Attitude Determination) algorithm obtains the direction cosine matrix relating both frames. The two vectors are typically the unit vector to the sun and the Earth s magnetic field vector (it can also be unit vector to two star using star tracker for example). This algorithm is not an optimal solution, but it provides a reliable estimation of the satellite s attitude while being quite cheap regarding computation needs. PPE-CDC-ADCS_1693 ECE Paris Page 31

f) Kalman Filter: The Kalman filter uses mathematical method to filter signal from noise or inaccurate measure. It is useful to determine position or orientation even with potential measurement errors. This filter can be used to filter, smooth or predict data (past/present/future). One of its advantage is that it provides an estimation of the error. In a discrete context, the Kalman filter is a recursive estimator: to estimate the current state it only needs the previous state and the current measures. To use Kalman filter, the system needs to be linearly modeled. But if the modeling is too approximate, the filter will not be efficient enough and the estimation error will not converge fast enough. The Kalman filter has 2 distinct states: Prediction (using the previous state it estimates the actual state) Correct (uses measurement to correct the predicted state) Figure 11 : The 2 states from the Kalman Filter An extended version of the Kalman filter exist, the principal difference being the possibility to use differentiable function instead of linear (for observation and prediction). PPE-CDC-ADCS_1693 ECE Paris Page 32

2. Sensors: Needs: Data redundancy Data for both situations: eclipse and sun Question of sampling frequency Location and size/weight Ability to resist to environment Low consumption Low price a) Gyroscope Micro Electro-Mechanical (MEM) Gyroscopes: MEMs gyroscopes have some form of oscillating component from where the acceleration and hence direction change, can be detected. This is because the conservation of motion law says that a vibrating object continues vibrating in the same plane, and any vibrational deviation can be used to derive a change in direction. Advantage: Compact Affordable Disadvantage: Noisy: drift ~0.5 per minute Figure 12 : Micro Electro-Mechanical (MEM) Gyroscopes PPE-CDC-ADCS_1693 ECE Paris Page 33

Stellar: This device tracks the motion of stars in the field of view. Stars are detected using the difference of color between pixels. Attitude propagation is based on successfully performing correspondence of these stars between camera frames. Advantage: Tolerates large amount of noise Can assist MEMS gyros by limiting drift Disadvantage: Figure 13 : Stellar Requires a digital signal processor on board the spacecraft Add computational requirement Too large for a CubeSat Ring Laser gyroscope (RLG): A ring laser gyroscope consists of a ring laser having two independent counter-propagating resonant modes over the same path; the difference in the frequencies is used to detect rotation. Advantage: High accuracy Disadvantage: Large Expensive Figure 14 : Ring Laser gyroscope (RLG) PPE-CDC-ADCS_1693 ECE Paris Page 34

Piezo Gyroscope: Use the deformation of a piezo electric bar to calculate the angle. Advantage: High accuracy Quick Lightweight Disadvantage: Vibration Need high speed processor Figure 15 : Piezo Gyroscope b) Gyrometer Gyrometer is an instrument which measures an angular acceleration. Two types exist: Optic A fiber optic gyroscope (FOG) senses changes in orientation using the Sagnac effect, thus performing the function of a mechanical gyroscope. However, its principle of operation is instead based on the interference of light which has passed through a coil of optical fiber which can be as long as 5 km. Advantages: Figure 16 : Optic Gyrometer extremely precise No moving parts => most reliable to the mechanical gyroscope Disadvantages: Requires calibration Too big for a CubeSat PPE-CDC-ADCS_1693 ECE Paris Page 35

Mechanic Thanks to rotation parts, it can use the inertial moment not to move the central access and calculate its inclination to the support. Advantage: No calibration needed Disadvantages: Doesn t work in space too big for a CubeSat (takes a lot of space) Figure 17 : Mechanic Gyrometer c) Sun sensor It is an optical device that detect the position of the sun. The photons coming from the sun enter in a photosensitive chamber. Using two sensors perpendicular to each other, the direction of the sun can then be determined. The output can be either discrete or analog. Sun Sensor IDD-Ax (analog) Advantages: High reliability Low power consumption Disadvantages: Figure 18 : Sun Sensor operation Accuracy (1 in Field of View of 30 ) PPE-CDC-ADCS_1693 ECE Paris Page 36

Coarse Bi-axis sun sensors Advantages: Low cost High strength High temperature range Standard FOV Disadvantages: Figure 19 : Bi-axis sun sensors They need direct sunlight (so they need to be on the sides of the CubeSat) d) Star tracker This optical device images a part of the sky and compares it to a map from the memory. This helps it to determine its orientation relatively to the stars Advantages: High accuracy Disadvantages: Need a reference map Need heavy data processing Size and weight (too much for a CubeSat) Figure 20 : Star Tracker PPE-CDC-ADCS_1693 ECE Paris Page 37

e) Horizon sensors Uses the relative difference between the dark of space and the light of earth to find earth s horizon. Advantages: Low cost Fast response time Disadvantages: Low accuracy (about 1 ) Figure 21 : Horizon sensors f) Magnetometer A Magnetometer is a device that measures a magnetic field. There is a lot of different methods to do so but some are better for CubeSat. Laboratory magnetometers Superconducting quantum interference device: Extremely sensitive but noise sensitive Inductive pickup coils: Detects the current induced in a coil Vibrating sample magnetometer (VSM): Uses vibration of sample inside a coil in order to detect induced current Heat due to vibration can be a constraint Fragile sample can be impractical Pulsed Field extraction magnetometer: Similar to VSM but this time it is the magnetic field that changes instead of the sample s vibration. Torque magnetometer: Indirect measure of magnetism: measures the torque resulting from a uniform magnetic field PPE-CDC-ADCS_1693 ECE Paris Page 38

Faraday force magnetometer: Uses gradient coils Optical magnetometer: Uses light on a sample which leads to an elliptical measurable trajectory Disadvantages: -Needs samples Survey magnetometers Scalar magnetometers (measures the strength of the magnetic field but not the direction: Proton precession magnetometer (uses nuclear magnetic resonance to measure the resonance frequency of protons) Overhauser effect magnetometer Caesium vapour magnetometer Potassium vapour magnetometer Vector magnetometers (measures the component of the magnetic field in a particular direction): Rotting coil magnetometer: Uses a rotating coil to induce a sin wave Old technology Hall effect magnetometer: Produces a voltage proportional to the applied magnetic field Used where the magnetic field strength is relatively large Magneto resistive devices Squid magnetometer Spin exchange relaxation free atomic magnetometers Fluxgate magnetometer PPE-CDC-ADCS_1693 ECE Paris Page 39

Fluxgate magnetometer The principle of this magnetometer is to use 2 coils: one is alimented with an alternative current, in the other coil the induced AC is measured (intensity and phase). When a change occurs in the external magnetic field, the output of the secondary coil is changed. This change can then be analyzed to determine the intensity and orientation of the flux lines. Advantages: Electronic simplicity Low weight Disadvantage: Can be sensitive to magnetic perturbations coming from inside the spacecraft RECAP magnetometers: Spacecraft magnetometers basically fall into three categories: fluxgate, search-coil and ionized gas magnetometers With the data collected from the magnetometer, we can with the B-Dot controller (or also the B bang bang) in link with the International Geomagnetic Reference Field (IGRF) determine the magnetic field vector. g) Temperature sensors A lot of measuring technologies exists: Thermometer: It is a device that measures temperature or a temperature gradient Bimetal: A Bimetal is an object that is composed of two parts of metal, joined together. When the temperature changes one of those two parts changes size which results in a deformation. The device measures this deformation. PPE-CDC-ADCS_1693 ECE Paris Page 40

Thermocouple: A thermocouple is an electrical device consisting of two different conductors forming electrical junctions at different temperatures. It produces a temperature dependent voltage as a result of the thermoelectric effect, and this voltage can be interpreted to measure the temperature. Resistance thermometers: Same as thermocouple, but the resistance changes value when the temperature evolves (it replaces thermocouples in industrial applications below 600 C) Silicon bandgap temperature sensor This extremely common sensor is used in electronic equipment. The main advantage is that it can be included in a silicon integrated circuit at very low cost. Here is the output voltage from the sensor: Where: T = temperature in Kelvin T0 = reference temperature VG0 = bandgap voltage at absolute zero VBE0 = junction voltage at temperature T0 and current IC0 K = Boltzmann s constant q = charge on an electron n = a device-dependent constant PPE-CDC-ADCS_1693 ECE Paris Page 41

h) Summary There is a lot of sensors, some of them need the sunlight, but as we will rotate around the Earth, we will also have to manage the CubeSat s attitude during the eclipse phase. Moreover, redundancy is a necessity for sensors. Figure 22 : Activity sensors in sun light and in eclipse The following figure presents the sensors which can be used in each case: Looking at this data some tendency can identified: We need two vectors during both the eclipse and sun lit phase. that is why the sensors we think to use would be: Sun sensor (to get sun vector but does not work while in eclipse) Magnetometer to get the magnetic field vector (also works while in eclipse) Another sensor for the eclipse phase (probably MEMS gyroscope) PPE-CDC-ADCS_1693 ECE Paris Page 42

3. Actuators: Needs: Physically act to modify attitude Compact design a) Reaction wheel Reaction wheels (RW) are primarily used by spacecraft for attitude control. The flywheel is attached to an electric motor, which makes it rotate when it moves. Due to the third law of newton the CubeSat will then start to counter-rotate. Because a reaction wheel can only make the CubeSat rotate around one axis, we would need 3 of them. Advantages: They are very efficient Disadvantages: It has to be close to the center of mass Needs too much energy and space to be accurate in a CubeSat. Figure 23 : reaction wheel b) Momentum wheel This device always spins at high speed to stabilize the spacecraft (gyroscopic effect). It makes the spacecraft resistant to changes relative to its attitude. PPE-CDC-ADCS_1693 ECE Paris Page 43

c) Control momentum gyroscope Works on the same principle as the reaction wheels do, but it can also change the spin axis (it's a sort of combination of reaction and momentum wheel). Advantages: Slightly more efficient than Reaction wheel (power consumption and torque) They are very efficient Useful for frequent and fast change of attitude Disadvantages: Figure 24 : Gyroscope Weight and size d) Magnetorquer Earth Magnetic Field The Earth's magnetic field is believed to be generated by electric currents in the conductive material of its core. It can be considered as a magnetic dipole as if there were a giant bar magnet placed at the center of the Earth. Figure 26 : Giant dipole The International Geomagnetic Reference Field called IGRF is a standard mathematical which describes this field with this series development: Figure 25 : IGRF with SciLab Where R is the Earth radius, r is radius vector, ф is satellite longitude, θ is latitude, P n m is Schmidt polynome. PPE-CDC-ADCS_1693 ECE Paris Page 44

There are several types of magnetorquers but only two designed for CubeSat: Linear magnetorquer (coil with an iron or nickel heart) and Integrated magnetorquers (inside of the solar panel). They create a magnetic field which interacts with the Earth s creating a torque. Indeed, magnetorquers are electrically supplied solenoids so the Ampere's theorem gives us a B field vector of the form: For a solenoid: For a torus: Typical values for a CubeSat: At 400 km, the magnetic field is approximately 25 µt (and 23 at 600 km). As our solenoids are in space, they interact with the Earth s magnetic field: A magnetic device is subject to a force: And a torque = ^ = ^ With I the intensity in the solenoid, S its surface, N the number of coils and B the Earth s magnetic field. Figure 27 : Magnetorquer operation PPE-CDC-ADCS_1693 ECE Paris Page 45

Advantages: Does not need electric current to work Light and efficient Disadvantages: The magnetic field generated can lead to false inputs and interpretations The attitude control on the 3 axes can be complicated because the torque will only be orthogonal to the Earth s magnetic field. e) Permanent magnet It is also possible to use passive actuators. One quarter of all CubeSat do use permanent magnet instead of magnetorquers. Permanent magnet is not precis with the angle to Nadir but are good enough to align on the magnetic field. Figure 28 : Evolution of the Nadir and Magnetic field angle from the CubeSat This graph shows that the angle to Magnetic Field is quickly stabilize but that the angle to Nadir is not at 90 degrees. It varies from 30 to 120 degrees. PPE-CDC-ADCS_1693 ECE Paris Page 46

4. Electronic board: State of the art The ADCS electronic board is composed of two parts: the hardware and the software. The hardware of the ADCS is a critical subsystem of the CubeSat. It has to combine the entire sensor system that the CubeSat needs in order to determine the satellite s attitude. It will run attitude determination and control algorithms. a) Hardware ADCS hardware has to: Get the sensor data. Process the data. Sample/correct them (for example Kalman filter). Determine the current attitude Determine the target attitude Control the magnetorquers to reach the target attitude. Handle the tether There are different hardware method to achieve the ADCS CTRL function. By using a FPGA card By using a PIC-Controller The FPGA card is more developed because it can calculate faster than a PIC and also it can handle a multiple signal treating. In a small satellite, as a CubeSat, the ADCS hardware can also be combined with the OBC. Usually even if the ADCS is on the OBC there is an actuator board to make the link between the ADCS and the OBC. One card is shown on the next figure. Figure 29 : example of ADCS board PPE-CDC-ADCS_1693 ECE Paris Page 47

b) Hardware constraint Space is a harsh environment, that is why the hardware has to be designed to withstand many constraints: It has to resist the temperature differences. In space, the temperature can fluctuate between -40 and 60 degree on the side panels and the temperature is around 10 to 40 degree inside of the satellite 1. The vacuum in space causes some materials destruction (especially plastic). If air bubbles are trapped in a component, it can create some cracks and in the worst case explode or damage components. The components are also exposed to radiations which can decrease the performance. And they are also exposed to ultraviolet radiations which can create some hardware failures. The hardware has to withstand high accelerations. Stay well oriented in order to let the tether deorbit our CubeSat. It also has to stay well oriented for the solar panels. 1 Data recorded in January 9th 2010 on the Ørsted satellite. Source: ADCS for AAUSAT3. PPE-CDC-ADCS_1693 ECE Paris Page 48

c) Software approach The software will handle the same functions that we enumerated for the hardware because both are very close. So obviously, the software will be designed to realize the same functions: Get the sensors data Process, sample and correct the data (Kalman Filter) Determine the target attitude with ADCS CTRL Algorithm Calculate the rotations to reach the target attitude Control the actuators to modify the attitude accordingly The CubeSat will be able to adapt in each situation thanks to an algorithm processing different states. State Sensor sampling Attitude estimation Control OFF NO NO NO SLEEP NO NO NO STANBY YES YES NO Tether ON YES YES ADVANCED DETUMBLE YES NO ADVANCED Pointing YES YES YES PPE-CDC-ADCS_1693 ECE Paris Page 49

5. Simulations We need to run simulations to validate our choice of components. In order to do this the software will have some constraints: Simulate the concerned part in the space environment (force models, vacuum, radiation, temperature ). Model parts of our system in blocks. Parameters (such as elevation, weight ) need to be modifiable. This is what we think could be useful for our project: Actuators sizing: The goal for the simulation software will be to validate actuator s specificity and reaction time. The aim is to choose the best actuator for CubeSat. This software needs some characteristics, at least: - A HCI (Human Control Interface) - A database to save tests. On the HCI we will be able to choose some variables: - CubeSat s information (elevation, mass, center of mass) - Coil s information (number of coils, number of layers, maximum electrical Power, coil s area) The software needs to run tests in different conditions: - Earth s magnetic field - CubeSat s rotation - CubeSat s orientation - Coil s alimentation time PPE-CDC-ADCS_1693 ECE Paris Page 50

To simulate our moving body in space condition, we consider using STK (Systems Tool Kit), which provides in the free version those features: As we can see this software is pretty complete and allows to run tests such as defining the trajectory of the satellite projected on earth, see the evolution of our satellite in space and mode sensors. Figure 30 : view in STK software PPE-CDC-ADCS_1693 ECE Paris Page 51

To fulfil the simulation s needs, we will also use other software such as Matlab/Scilab. Those software will be useful to draw block diagrams, leading to exploitable data. Moreover, some code or complementary modules can be implemented for precise simulations. For example, the Control Toolbox module provides interesting tools for CubeSat missions such as: PPE-CDC-ADCS_1693 ECE Paris Page 52

VII. Planning Figure 31 : Gantt planning PPE-CDC-ADCS_1693 ECE Paris Page 53

VIII. Technical sizing PPE-CDC-ADCS_1693 ECE Paris Page 54

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IX. Existing CubeSat PPE-CDC-ADCS_1693 ECE Paris Page 57

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